Answer

There is no specific time since every dalmation gets their spots at their own pace.

Dalmatian pups are born completely white, but if you look closely you can see the darker/grayish looking spots around their body. Pups that are born with black have 'patches', which don't impress in the showing ring although they do give more variation and character in individuals. As they age to about 2 weeks, their spots will begin to take a more noticeable color. You'll notice throughout the first year that their spots will become darker and larger. Spots that are clustered together will probably turn out looking like a patch when they're fully grown, but this patch-look-a-like is not considered as a patch.